In a sequence a1, a2,…, each term after the first is found by taking

Question

In a sequence a1, a2,…, each term after the first is found by taking the negative of the preceding term, and adding 1. If a1 = 2, what is the sum of the first 99 terms?

(A) 49
(B) 50
(C) 51
(D) 99
(E) 101

pushpitkc · Answer

In the sequence, since a1 = 2, a2 will be equal to (-2) + 1 = -1.
Similarly, a3 is -(-1) + 1 = 2 and a4 = -2 + 1 = -1.

We see a pattern emerge where the odd term is 2 and the even term is -1.
The sum of every pair of odd and even term is 1. The first 99 terms contain
49 pairs of even and odd terms and the 99th term.

Therefore, the sum of the first 99 terms is 49*1 + 2 =   51(Option C)

niks18 · Answer

a_1=2 => a_2=-2+1=-1, a_3=-(-1)+1=2, a_4=-2+1=-1, a_5=-(-1)+1=2 , and so on

So we see here all the Odd terms are same and equal to  2  and all the even terms are same and equal to  -1

from  1  to  99 , there are  49  even terms and  50  odd terms.

Hence the sum  = 50*2+49*(-1)=51

Option  C

JeffTargetTestPrep · Answer

a1 = 2

a2 = -1

a3 = 2

a4 = -1

a5 = 2

a6 = -1

We see that each odd/even pair sums to positive 1.

There are 49 even/odd pairs in the first 98 terms; hence, the sum is 49. Since a99 is an odd-numbered term, a99 = 2. So the sum of the first 99 terms is 49 + 2 = 51.

Answer: C

akadiyan · Answer

In a sequence a1, a2,…, each term after the first is found by taking the negative of the preceding term, and adding 1. If a1 = 2, what is the sum of the first 99 terms?

A1 = 2
A2 = -2 + 1 = -1
A3 = -(-1)+1 = 2
A4 = -2+1 = -1

The pattern repeats. If you add A1+A2 you get 1, so similarly there are 49 pairs in first 98 numbers - 49 , the 99th term is 2

Ans: 49 + 2 = 51

Ans:  C

ingy · Answer

why can't use the sum of terms rule here . Sum= number ( first + last) / 2 , instead of checking the pattern.

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